Can someone help me to better understand energy

[Pattonias]

I think that until this point I have always held the misconception that energy was the transfer of electrons, but I have come to realize my mistake. I have tried using wikipedia's definition of energy to better understand, but I don't think I am really getting it.

When you take a measure of energy what exactly are you measuring? Is energy a term that describes several different phenomena?

 

[mgb_phys]

The normal definition is that "energy is the capacity to do work" which is completely useless, since the only way of defining work is the same statement.

The technical definition of energy is do with entropy - but gets a bit complicated.
A good way to think about it is that energy is what you need to put into a system to put it into a less stable or more disordered state

 

[Pattonias]

Don't worry, I really want to get into the actual definitions of energy. If you end up going over my head I'll do the reading I need to better understand. I want to be an engineer and I want to specialize in physics so I will have to really understand this eventually.

Complicated is good, if the eventual result is my understanding how energy operates this thread will be a success.

 

[James Leighe]

Don't worry, I really want to get into the actual definitions of energy. If you end up going over my head I'll do the reading I need to better understand. I want to be an engineer and I want to specialize in physics so I will have to really understand this eventually.

Complicated is good, if the eventual result is my understanding how energy operates this thread will be a success.

It's not complicated luckily. Energy is the thing that never goes up or down in a closed system, no matter what happens. It can 'convert' between many forms, but when you add all the values for the different forms up (kinetic, potential, electrical, chemical) it should always be the same in a closed system.

 

[dsol]

As an aside, most engineers do not need to know what energy "is". I assume you are an early undergraduate student in engineering, and I am basing the following statements on that assumption:

Take it from someone who spent way too much time trying to understand the minutia of physics in his undergraduate engineering classes. Unless you are going to be in a very specialized electrical engineer, it will not matter what "energy is". Indeed, if your job depends on this understanding, most likely you are a scientist rather than an engineer. As an engineer, you absolutely must know what sources of energy you have, and how that energy behaves (ie: how it is transferred from one state and/or object to another), but you do not need to know what energy is truly based on.

While I am warning not to get obsessed with this matter at the expense of learning other more applicable knowledge, I do applaud your curiosity, and hope you find the answer you are searching for.

 

[mgb_phys]

Energy is the thing that never goes up or down in a closed system, no matter what happens.

So how is that different from angular momentum, spin, parity or charge?

 

[Pattonias]

Could 0 Kelvin be described as the absence of energy?

 

[James Leighe]

So how is that different from angular momentum, spin, parity or charge?

Well, damn...
Angular momentum is kinetic so I guess that fits in pretty well. As for spin and charge, they could be lumped into conservation of energy right? Since those values are also conserved it would make no difference I think. And parity is a symmetry relationship, and I don't know how it would fit in but I'm guessing it could similarly.

Seems like there is some arbitrary-ness in the distinction IMO. But I'm probably profoundly wrong.

 

[James Leighe]

Could 0 Kelvin be described as the absence of energy?

I don't think you can do that, there is something called the 'zero-point' energy, which is simply the minimum energy that the system can have. But assuming you could get to zero kelvin, yeah, it would be pretty much the absence of energy... you could freeze stuff out of existence! (once again warning on profound wrongesses)

 

[Gerenuk]

When you take a measure of energy what exactly are you measuring? Is energy a term that describes several different phenomena?

For all practical purposes all energies that we know are one of the following

• kinetic energy due to speed of some massive object (or atoms or electrons)
• potential energy due to a force (gravitation between masses, electrostatic between charged objects, magnetic dipoles in magnetic field) between each pair of objects
• energy from electromagnetic waves (light, radio waves, x-rays)
• mass energy according to E=mc^2

There is no other.
Not all energy is extractable though, since the second law of thermodynamics can constrain which energy you will be able to extract by any real process.
And energy is conserved (this can achieved by fiddling with the definition of potential energy)

 

[Gerenuk]

Could 0 Kelvin be described as the absence of energy?

Apart from quantum mechanics ideas about zero point energy, classically 0K could be taken as the statement, that there is no "kinetic energy" (see my first point). You still can have "potential energy" and "mass energy".

And btw, chemical energy is a combination of mass energy and potential energy.

 

[Lsos]

I think that until this point I have always held the misconception that energy was the transfer of electrons, but I have come to realize my mistake. I have tried using wikipedia's definition of energy to better understand, but I don't think I am really getting it.

When you take a measure of energy what exactly are you measuring? Is energy a term that describes several different phenomena?

"What is energy" is kind of a fundamental question, which I'm not sure can be answered in a way that would satisfy you. It's kind of like..."what is mass". "What is space". "What is existence".

At least that's my take on it. Maybe there is some finite answer rooted deep in quantum physics, but either way I don't think you or me will find a true understanding of it. At least yet.

 

[Dale]

The normal definition is that "energy is the capacity to do work" which is completely useless, since the only way of defining work is the same statement.

Why do you say that? Work is force times distance. It is easy to define non-circularly.

 

[A.T.]

When you take a measure of energy what exactly are you measuring?

You never measure energy directly. Energy is an abstract concept, just like force. It is an quantity that you calculate from measurable quantities. It is useful because it is constant for a closed system.

 

[Dadface]

I think that until this point I have always held the misconception that energy was the transfer of electrons, but I have come to realize my mistake. I have tried using wikipedia's definition of energy to better understand, but I don't think I am really getting it.

When you take a measure of energy what exactly are you measuring? Is energy a term that describes several different phenomena?

If it moves or if it can make things move it has energy.Look around you,everything you can see and things which you can't see but which you know are there has energy.The mouse on your desk has energy,the full stop at the end of this sentence has energy,everything has energy.Matter is the stuff and energy the thing that can move the stuff. Even when it's stationary matter has stored energy because it is able to make things move.
It's more complicated than this and to get a fuller understanding you need to look at the definition of work,the different forms of energy and how they are calculated and,most interestingly,the conservation of energy.

 

[Pattonias]

So energy is not any single thing/substance. It is a term used to describe anything that has movement or the ability to move. Is this a correct statement? Does energy stop being a factor when you remove time from the equation?

 

[Dadface]

So energy is not any single thing/substance. It is a term used to describe anything that has movement or the ability to move. Is this a correct statement? Does energy stop being a factor when you remove time from the equation?

Like my description above I would say it's a reasonable statement but to define energy properly you need to get mathematical.I don't know how to remove time from the equation but ,and this is a total guess,I am assuming that for many engineering applications a highly detailed knowledge of energy may not be necessary.

 

[bp_psy]

So energy is not any single thing/substance. It is a term used to describe anything that has movement or the ability to move. Is this a correct statement? Does energy stop being a factor when you remove time from the equation?

If you remove time from the equation then you remove physics from the equation.
I do not understand why so many people come up with this "time removal" idea.Why not space removal? It is as essential to physics as time but nobody asks "What happens when we remove space from the equation?"

 

[Gerenuk]

So energy is not any single thing/substance. It is a term used to describe anything that has movement or the ability to move. Is this a correct statement? Does energy stop being a factor when you remove time from the equation?

Not a single at least. Movement (kinetic) is OK. Ability to move is very vague. Let's say is the contribution from all forces pull that object. Now you should also include that every mass has an energy, and that electromagnetic waves have an energy. Then you are indeed correct.

It's rather hypothetical, philosophical but true: the energy concept is useless if you have only one instant of time. Energy was invented to have a new parameter which is independent of time and can help you to solve problems.

 

[Pattonias]

Its not so much that I feel that I would need to have a firm grasp of energy to be an engineer, but I want to have a firm grasp of energy. I don't know if I can express how stupid I felt at having though energy always had to do with the transfer of electrons from one thing to another. That was a misconception that made Chemistry rather difficult.

Energy is not something that can be put into a bucket and weighed. We only know of its existence from its effects from one object to another. Right?

 

[Gerenuk]

Energy is not something that can be put into a bucket and weighed. We only know of its existence from its effects from one object to another. Right?

I'd agree.
In the classical picture at least it's merely a mathematical trick to obtain a new constant of motion.

 

[A.T.]

Energy is not something that can be put into a bucket and weighed.

Actually that works for a certain form of energy: energy is equivalent to mass.

We only know of its existence from its effects from one object to another.

I prefer to say: "We use the concept of energy to describe these effects"

"Existence" is a difficult term. Do numbers exist? Just like them, physical quantities are abstract concepts made up by humans. They are properties humans assign to existing things, rather than an existing things.

 

[Pattonias]

I'm just thinking about how much of a difference this makes to my understanding of E=mC^2...

What kind of energy is produced when matter is converted to energy. I know that their is a lot of it (i.e. nuclear explosions), but what form of energy is produced? All forms?

 

[jambaugh]

Let me give it a go...

I'll start with the most abstractly technical and least intuitive definition.
Energy is the Noether charge necessarily conserved for dynamical systems with time translation symmetry.

To break that down let me explain a "Noether charge". Emma Noether in helping Einstein with some issues of what is conserved in his new theory developed a beautiful theorem now named after her that shows in rough terms:
The dynamics of a physical system has continuous symmetry if and only if there is a corresponding conserved quantity.

The classic examples are:
Symmetry---------------Conserved Quantity
Rotational symmetry <---> Angular Momentum
Spatial Translation<---> Linear Momentum
Time Translation <---> Energy

Note that since in Special Relativity space and time are unified, so too is energy and linear momentum, dual to the four space-time translation symmetries are the four momentum-energy components which are conserved. When we get to General Relativity the symmetries grow and we get a larger set of conserved quantities namely Stress-Energy which is a 4x4 symmetric tensor (matrix) containing energy, momentum and some other more abstract but related quantities.

More esoteric examples exist as well. In gauge theory we invoke an abstract internal symmetry and this defines a conserved charge.
With the Standard Model we have:

U(1) (complex phase) <---> Electric Charge
SU(2)(weak iso-rotations)<---> Weak Isospin
SU(3)(strong gauge)<---> quark color

This Noether correspondence between symmetries and conserved quantities provides a very powerful tool for formulating new theories. Physicists may hypothesize symmetries and they look for the conserved charges, or they see conserved charges and they invoke a symmetry which gives them a great deal of information about the physical behavior.

OK, now given all that high brow stuff, what does "energy" mean? Firstly it is a physical observable which means it is something you can measure for a given system. Staying in the classical realm for now you can think of any physical observable as being some function of a system's physical state. Knowing the state is the same as knowing the value of all physical observables.

A physical observable is conserved if whenever systems interact and their observables change values the net total of a given conserved quantity does not change. Thus if you consider an (elastic) collision between two balls figure out their total energy before the collision and that will be the total energy after the collision.

Finally knowing what function of the physical system defines a given conserved quantity, you can deduce how the system state description must change under the corresponding symmetry transformations. In particular knowing the energy tells us how the system transforms as time passes.

The energy function defines the dynamic evolution.

This is how we know which of many conserved quantities is which, by identifying them with the transformations they describe. This procedure where we use the energy to determine the dynamics as opposed to solving for it directly from forces and their relationship to rates of change, is known as Hamiltonian mechanics.

Well I hope this at least put the concept into some context for you.

In summary: Energy is a conserved quantity which when known as a function of the system description gives us the dynamic evolution of the system over time.

This is essentially the same as the original definition I gave but hopefully more understandable now.

 

[jambaugh]

Actually that works for a certain form of energy: energy is equivalent to mass.

Not quite accurate. The famous equationE = mc^2 is just a special case in the rest frame of a particle. The full equation is:

E = \sqrt{m^2 c^4 + \mathbf{p}^2c^2}
where \mathbf{p} is the momentum. In more natural form the equation is:
E^2 - (c\mathbf{p})^2 = (mc^2)^2

In terms of my prior post, mass is "proper energy" corresponding to proper time translation while energy corresponds to time translation in the observer's frame. Thus different observers will see different energies but all agree on the "proper energy"= mass which is the energy seen by an observer comoving with the particle in question.

 

[Pattonias]

I really appreciate the extended explanation. While I don't immediately know all the references and principles that you have laid out, I can use this as a starting point for more reading.

Another question.

Can and does energy exist apart from matter? And if it does then in what form? Can it attach itself to matter that it comes in contact with?

 

[A.T.]

Energy is not something that can be put into a bucket and weighed.

Actually that works for a certain form of energy: energy is equivalent to mass.

Not quite accurate. The famous equationE = mc^2 is just a special case in the rest frame of a particle. (...) In terms of my prior post, mass is "proper energy"

Isn't proper energy a "certain form of energy?" And putting something into a bucket to weight it, is usually done in it's rest frame.

 

[A.T.]

Can and does energy exist apart from matter? And if it does then in what form?

Antimatter! And usually radiation (EM-waves) is not considered to be matter, but has energy.

Can it attach itself to matter that it comes in contact with?

Yes, radiation can heat up matter for example.

 

[Pattonias]

Antimatter! And usually radiation (EM-waves) is not considered to be matter, but has energy.

Yes, radiation can heat up matter for example.

Radiation is not pure energy though, is it not carried by one form of matter or another as excited particles?

I guess a better question would be, can energy travel independent of matter?

 

[A.T.]

Radiation is not pure energy though, is it not carried by one form of matter or another as excited particles.

As I said, usually EW-waves / photons are not considered to be matter. Usually things with rest mass are called matter or antimatter.

I guess a better question would be, can energy travel independent of matter?

Besides EM-waves? Nothing comes to my mind.

 

[Pattonias]

Ok, I'll read a bit about EM-waves.

 

[jambaugh]

I really appreciate the extended explanation. While I don't immediately know all the references and principles that you have laid out, I can use this as a starting point for more reading.

Another question.

Can and does energy exist apart from matter? And if it does then in what form? Can it attach itself to matter that it comes in contact with?

Gets tricky here qualifying things like this. You can define "matter" as anything which possesses energy (above the vacuum) and even then you can speak of the vacuum itself containing "matter" (like the Dirac sea).

But the best answer I can say is that every system has an energy even a block of empty space. Energy is a property, the value may be zero but that doesn't mean "there is no Energy". You can also in most cases speak of energy in a relative sense. I.e. it is changes in energy that are important not the absolute value.

The cosmological constant basically is a way of absorbing such resetting of the zero value while still giving meaning to the energy affecting space-time curvature. You can "reset" the zero energy (density) plus change the value of the cosmological constant to effect equivalent gravitational effects. (I make it sound simple but its tricky doing this. One also has to play with the definition of inertial mass when working with non-gravitational forces.)

 

[Dale]

I really don't think it is so complicated. Energy is the capacity to do work, work is force times distance. jambaugh is correct that there are all sorts of interesting advanced topics, but none of it changes the fundamental definitions, especially not at the level of the OP.

 

[Phyisab****]

I just want to say that Jambaugh, that was a very good explanation.

 

[stevefaulkner]

Would it be true to say that energy is the only conserved quantity that transforms as a scalar?

 

[Gerenuk]

Would it be true to say that energy is the only conserved quantity that transforms as a scalar?

If you consider frame transformations, which is different from the time evolution transformations, then any product of two vectors is a scalar (rest mass of a particle, ...).

Not sure how this refers to time evolution transformation. I think in general energy, momentum and angular momentum are the only integrals of motion unless you deal with a special problem.

Edit: Oh, I see. You meant something that is both
Then in general only energy should be the conserved scalar. Unless the problem is a special one.

 

[jambaugh]

Would it be true to say that energy is the only conserved quantity that transforms as a scalar?

Not at all. Firstly it is only scalar in a non-relativistic setting. In SR energy is one component of the 4-vector energy-momentum. Electric charge and the other gauge charges are space-time scalars (with some slight qualification on weak isospin due to weak parity issues).

The nice part of the link between conserved quantities and symmetry transformations is that how the quantities transform (whether they are scalar, vector, tensor, ...) with respect to the various groups (rotation, Lorentz, Poincare, ...) is made explicit by how the symmetry transformations themselves transform. Consider that translation in the x direction can be rotated to translation in e.g. the y direction. Hence rotations act not only in concert with translations on objects, but also rotations act on translations. This is called the adjoint action of one transformation on another.

Since time translation is "scalar" i.e. invariant under spatial transformations (rotations and spatial translations) Energy is scalar in this non-relativistic setting. Since spatial translation in a given direction gets rotated by a rotation transformation so does momentum. Momentum is a vector quantity.

In the relativistic setting you can think of energy as "momentum in the time direction" and Lorentz transformations act on the four momenta as a 4-vector.

One final note. You can imagine for some system that you can "tweak" the dynamics to have any arbitrary symmetry or that you break a given symmetry. This does not interfere with the link between measurable quantities (which may or may not be conserved) and transformations (which may or may not be symmetries).

EDIT: In short the link is there without worrying about the quantity being conserved or the transformation being a symmetry :END EDIT

This is made most explicit in the formulation of quantum mechanics where the operators generating the transformations are identified mathematically with the operators corresponding to the observables.
The momenta ARE the generator of translations,
Energy (the Hamiltonian) IS the generator of time evolution,
Angular Momenta ARE the generators of rotations.

It is all very elegant and beautiful. That it also yields an accurate description of how nature behaves is gravy on the biscuit!